The question of Iago’s motivation reverberates through the play and the history of its criticism. How do you understand the character’s motives?

I tend to think that it is envy that drives Iago.  He
feels slighted that Cassio received favor over him and is willing to do what is needed
to ensure that everyone feels this pain through his wrathful manipulation. I think that
the question is right in asserting that his scheming reverberates throughout the play. 
Part of this lies in the fact that Iago is the only character who is openly
communicative with just about everyone in it.  Contrary to most villains, he is not one
to isolate others, rather bringing them into his plan and schemes.  In this light, Iago
becomes quite a dangerous force in that his scheming knows no boundaries and afflicts
everyone.  It is this desire to impact others, to compel them to feel his own pain, and
to ensure that allows for his motivation to be understood in a totalizing
manner.